12/2/2011. Estimated number of age class alive. Proportion of individuals surviving at start of interval

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1 Life Tables: Like projection matrices, another way to account for age/stage specific survivorship patterns in a population. When paired with fecundity data estimation of growth rates, stable stage distribution, and lifetime reproduction possible. Estimated number of age class alive Number of age Finite rate of class found dead mortality during interval Proportion of individuals surviving at start of interval Proportion of individuals in each stage/age at ssd/ssa distribution (must have fecundity data to estimate lambda) 1

2 Types of Life Tables Cohort or age-specific or dynamic life tables: data are collected by following a cohort throughout its life. This is rarely possible with natural populations of animals. Note: a cohort is a group of individuals all born during the same time interval. Static or time-specific life tables: age-distribution data are collected from a cross-section of the population at one particular time or during a short segment of time, such as through mortality data. Resulting age-specific data are treated as if a cohort was followed through time (i.e., the number of animals alive in age class x must be less than alive in age class x-1). Because of variation caused by small samples, data-smoothing techniques may be required (see Caughley 1977). Composite - data are gathered over a number of years and generations using cohort or time-specific techniques. This method allows the natural variability in rates of survival to be monitored and assessed (Begon and Mortimer 1986). Life Tables: Survivorship curves are often created from life table data, plotting the proportion of a cohorts individuals alive (l x ) over time. Three common patterns of survivorship are seen in populations (but others exist). Description/example of each? Begon and Mortimer (1996) 2

3 Measuring/Estimating Demographic Parameters: Reproduction, births, natality (B) Immigration (I) Population Emigration (E) Mortality, death (D) Births / Fecundity Natality: Average number of live offspring born to individuals that reproduce Fecundity: Average number of offspring (usually female) born per individual (usually female) Fecundity = Natality x proportion of population that gives birth How do we measure this for different taxa? 3

4 Estimating fecundity Field methods: Direct counts of young observed in utero: ultra sound, placental scars after birth: in dens, nests, schools, etc Indirect Number of young inferred from some component(s) of reproduction (clutch size, nest/hatching success, etc) Landscape specific fecundity estimates: From spot-mapping data and nest monitoring Territory success rates Number of fledglings/ successful nest These numbers used to estimate fecundity Song Sparrow Reserves Changing Developed % Successful % 2 nd Brood Fledglings/nest attempt Fledgling/female (Oleyar & Marzluff unpub data) Fecundity = (% successful * mn fledglings) + (% 2 nd brood * mn fledglings)/2 4

5 Estimating fecundity Analytical methods (mark-recapture): Jolly-Seber open population (Program MARK) : estimates number of individuals added to population (if assume no immigration then that number is births) Ratios of juveniles to adults: gives an index of yearly reproduction and if stable age/stage distribution is assumed/known, then can be used to calculate numbers in each class and estimate fecundity Mortality / Survival Survival rate = (1 - Mortality rate) **Survival estimators generally arise from 3 types of data: 1) All animals can be relocated (known fate) and determined to have survived or died 2) Only survivors are encountered (e.g., capturemark-recapture) 3) Only deaths are recorded (e.g., band recovery) 5

6 Mortality / Survival Known-fate Model Kaplan-Meier method: Individuals in the population are monitored (e.g., via telemetry) over time Accommodates 'staggered' entry into the known population Animals may be 'censored' (i.e., leave the known population) Survival can change over time (due to harvest, seasons, etc.) Kaplan-Meier Survival: Time Period At Risk Became Unavailable (Censored) Died Survived Kaplan-Meier Survival Probability Estimate Year (95/100)=0.95 Year Year Year = x(64/79)=0.70 = Year x(13/38)=

7 Kaplan-Meier Survival: Time Period At Risk Became Unavailable (Censored) Died Survived Kaplan-Meier Survival Probability Estimate Year (95/100)=0.95 Year Year Year = x(64/79)=0.70 = Year x(13/38)= Kaplan-Meier Survival: Time Period At Risk Became Unavailable (Censored) Died Survived Kaplan-Meier Survival Probability Estimate Year (95/100)=0.95 Year Year Year = x(64/79)=0.70 = Year x(13/38)=

8 Kaplan-Meier Survival: Time Period At Risk Became Unavailable (Censored) Died Survived Kaplan-Meier Survival Probability Estimate Year (95/100)=0.95 Year Year Year = x(64/79)=0.70 = Year x(13/38)= Mark-recapture Cormack-Jolly-Seber method: Open population model Use Program MARK to run analyses Accommodates 'staggered' entry into the known population Animals may be 'censored' (i.e., leave the known population) Survival can change over time (due to harvest, seasons, etc.) Assume NO emigration... Underlying concept: Recapturing/resighting a marked animal is a product of 2 probabilities: 1) The probability that the animal is alive and still in the study area apparent survival vs true survival 2) The probability of capturing/encountering the animal during a sample period 8

9 Mark-recapture Cormack-Jolly-Seber method: Open population model Use Program MARK to run analyses Accommodates 'staggered' entry into the known population Animals may be 'censored' (i.e., leave the known population) Survival can change over time (due to harvest, seasons, etc.) Assume NO emigration... Where: M-hat i = size of marked population at time i m i = number marked at time i (recaps) Where: R i = number of marked individuals released at i r i = number released at i that are captured again z i = number captured prior to i and caught again later, but not caught during i 9

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12 Band Recovery Based on Mark-Recapture Methods Recoveries are only dead individuals 12